> And yeah, the development of sati, along with other helpful factors, can help to gain insight, which is basically the way the mind looks at itself and conceptualises its own experience, in a kind of self-reflective way

Actually the insight of vipassana is pretty consistent in being other-reflective and not "self"-reflective. It's concentrating on mental states as they happen, and realizing that a mental state can never be truly "about" itself, but at most it can relate to the fleeting memory of a former mental state. Since there is thus no such thing as actual "self"-reflection, the next insight is that mental perceptions, at their most basic level, do not in fact evidence any continuity and distinct identity of the "self" - which is of course the core "insight" of anatta!